Problem: Takahashi loves sorting.

He has a permutation (p_1,p_2,...,p_N) of the integers from 1 through N. Now, he will repeat the following operation until the permutation becomes (1,2,...,N):

* First, we will define high and low elements in the permutation, as follows. The i-th element in the permutation is high if the maximum element between the 1-st and i-th elements, inclusive, is the i-th element itself, and otherwise the i-th element is low.
* Then, let a_1,a_2,...,a_k be the values of the high elements, and b_1,b_2,...,b_{N-k} be the values of the low elements in the current permutation, in the order they appear in it.
* Lastly, rearrange the permutation into (b_1,b_2,...,b_{N-k},a_1,a_2,...,a_k).



How many operations are necessary until the permutation is sorted?

Constraints

* 1 ≤ N ≤ 2×10^5
* (p_1,p_2,...,p_N) is a permutation of the integers from 1 through N.

Input

Input is given from Standard Input in the following format:


N
p_1 p_2 ... p_N


Output

Print the number of operations that are necessary until the permutation is sorted.

Examples

Input

5
3 5 1 2 4


Output

3


Input

5
5 4 3 2 1


Output

4


Input

10
2 10 5 7 3 6 4 9 8 1


Output

6

Solution (in CPP):

Solution:
#include <stdio.h>

int N,pos[200200],T[200200],F[200200];

int main()
{
	scanf ("%d",&N);
	for (int i=0;i<N;i++){
		int x; scanf ("%d",&x);
		pos[x] = i;
	}

	T[N] = F[N] = 0;
	for (int i=N-1;i>=1;i--){
		if (T[i+1] == 0){
			if (pos[i] < pos[i+1]) T[i] = F[i] = 0;
			else T[i] = 1, F[i] = i+1;
		}
		else{
			if (pos[i] < pos[i+1] && pos[i+1] < pos[F[i+1]]
				|| pos[i+1] < pos[F[i+1]] && pos[F[i+1]] < pos[i]
				|| pos[F[i+1]] < pos[i] && pos[i] < pos[i+1]) T[i] = T[i+1], F[i] = F[i+1];
			else T[i] = T[i+1] + 1, F[i] = i+1;
		}
	}

	printf ("%d\n",T[1]);

	return 0;
}